Revision 2 into the paper.

2: 'pre-registered' -> 'recorded in advance'; Appendix D states the order is attested only by the author's git history. 3: Dekker, Illinois and false position exhaust the budget on aps.13.00 under either criterion (stalled where |f|<1e-62, no sign change within 1e-6) - hence unchanged totals. 4: exact-zero stops in Table 11 (CHA: Brent 15/20, Chandrupatla 4/20, A' 2/20; corpus 1: none, transformation still 3.4x cheaper). 5: Table 12, the multiplicity estimated during the run (A' ahead; the analogy order inside Chandrupatla closes 31-59% of the gap on multiple roots and pays on simple ones; Lagouanelle blind on side-alternating triples); 6.6, conclusion, future work. 6: Algorithms 1-2 - lo/hi, return on a stall, L_x/L_f and the empty memory, the step pattern as a formula, O(n^2). 7: Table 3's two bracket-scaled rows, dashes in Table 5, the abstract's last sentence (250 words). verify_revision2: 17 checks. Server: verify 544 OK / 0 BAD, regression x2 1238 passed, PDF 32 pages, 0 errors, 0 overfull.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

apply_verify_revision2.py

@@ -0,0 +1,106 @@
+"""verify_article.py checks the numbers the second revision added: Table 12 and its paragraph
+(sweep_estimated.json), the exact-zero stops of Table 11 (diag_revision2.point4, fresh), the three
+unchanged rows of Table 2 (fresh runs on aps.13.00), the two new rows of Table 3, and the fractional
+readings of Lagouanelle's estimate on the canonical set (fresh).  Adds verify_revision2() and its call.
+
+    python -u apply_verify_revision2.py
+"""
+PATH = "verify_article.py"
+FUNC = '''
+
+def verify_revision2():
+    """Revision 2 (points 3, 4, 5, 7)."""
+    import math
+    print("\\nRevision 2:")
+
+    def cost(v):
+        return v[0] if v[1] else 200
+
+    def tot(r, keep=None):
+        return sum(cost(v) for p, v in r.items() if keep is None or keep(p))
+
+    def sign_p(w, l):
+        k, n = min(w, l), w + l
+        return min(1.0, 2.0 * sum(math.comb(n, i) for i in range(k + 1)) / 2.0 ** n)
+    sets = ("APS", "CHA", "NEW", "RJL", "APP", "D")
+    K = _load("sweep_estimated.json")
+    seen, four = _load("sweep_fourth_seen.json"), _load("sweep_fourth_fourth.json")
+    ap, ch = dict(seen["Aprime"]), dict(seen["chandrupatla"])
+    ap.update(four["Aprime"])
+    ch.update(four["chandrupatla"])
+    K1 = _load("sweep_controls.json")["K1"]
+    nonsimple = lambda m: m >= 2.0 or m <= 2.0 / 3.0  # noqa: E731
+
+    def group(r):
+        return sum(tot(r[s], lambda p, _m=K1[s]["mstar"]: nonsimple(_m[p])) for s in ("CHA", "NEW", "D"))
+    rows = {"A'": ap, "K3A": K["k3_analogy"], "K3L": K["k3_lag"], "Ch(f)": ch}
+    want = {"A'": (3656, 13032, 4042, 2259), "K3A": (3806, 15733, 2809, 3453),
+            "K3L": (7526, 30991, 6041, 7215), "Ch(f)": (5717, 16481, 7011, 2595)}
+    for k, r in rows.items():
+        check(f"Table 12 {k}", (tot(r["D"]), sum(tot(r[s]) for s in sets), group(r), tot(r["APS"])), want[k])
+    oracle = sum(tot(K1[s]["chandrupatla_g"], lambda p, _m=K1[s]["mstar"]: nonsimple(_m[p]))
+                 for s in ("CHA", "NEW", "D"))
+    check("Table 12 oracle row (Table 11 sum)", oracle, 1355)
+    ps = list(ap["D"])
+    w = sum(cost(ap["D"][p]) < cost(K["k3_analogy"]["D"][p]) for p in ps)
+    l = sum(cost(ap["D"][p]) > cost(K["k3_analogy"]["D"][p]) for p in ps)
+    check("A' vs Chandrupatla-on-g with the analogy order, corpus 4", (w, len(ps) - w - l, l), (126, 38, 76))
+    check("its p (1 digit)", f"{sign_p(w, l):.1g}", "0.0005")
+    shares = []
+    for s in ("CHA", "NEW", "D"):
+        keep = lambda p, _m=K1[s]["mstar"]: nonsimple(_m[p])  # noqa: E731
+        a_, k_, o_ = tot(ap[s], keep), tot(K["k3_analogy"][s], keep), tot(K1[s]["chandrupatla_g"], keep)
+        shares.append((k_, a_, round(100 * (a_ - k_) / (a_ - o_))))
+    check("share of the A'-to-oracle gap closed by the analogy order", shares,
+          [(322, 654, 59), (721, 1229, 58), (1766, 2159, 31)])
+    check("K3 bound violations", sum(v[2] for k in K for s in sets for v in K[k][s].values()), 0)
+    # Lagouanelle's fractional readings on the simple roots of the canonical set (fresh)
+    from simroot.transformed import chandrupatla_transformed
+    from sweep_full import load_problems
+    frac = 0
+    for s, pid, f, a, b, _r in load_problems():
+        if s != "APS":
+            continue
+        st = {}
+        chandrupatla_transformed(f, a, b, 1e-12, 200, estimator="lag", stats=st)
+        m = st.get("m_hat", 1.0)
+        frac += (0.0 < m <= 2.0 / 3.0)
+    check("Lagouanelle holds a fractional order on simple APS roots", frac, 115)
+    # point 4: exact-zero stops (fresh)
+    import contextlib
+    import io
+    import diag_revision2
+    with contextlib.redirect_stdout(io.StringIO()):
+        z = diag_revision2.point4()
+    check("exact-zero stops on CHA: Brent(g), Chandrupatla(g), A'",
+          (z["CHA"]["brent_g"][1], z["CHA"]["chandrupatla_g"][1], z["CHA"]["Aprime"][1]), (15, 4, 2))
+    check("exact-zero stops of the transformed runs on corpus 1",
+          (z["NEW"]["chandrupatla_g"][1], z["NEW"]["brent_g"][1]), (0, 0))
+    check("corpus 1: transformation 3.4 times cheaper", round(1229 / 358, 1), 3.4)
+    # point 3: the three unchanged rows of Table 2 (fresh)
+    from corpus_roots_jl import solved
+    from sweep_full import make_method
+    f, a, b = next((f, a, b) for s, pid, f, a, b, _r in load_problems() if pid == "aps.13.00")
+    got = []
+    for name in ("dekker", "illinois", "regula_falsi"):
+        x, n, conv = make_method(("base", name))(f, a, b, 1e-12, 200)
+        got.append((name, int(n), bool(conv), bool(solved(f, float(x)))))
+    check("aps.13.00: Dekker, Illinois, false position spend the budget unsolved",
+          got, [("dekker", 200, False, False), ("illinois", 200, False, False),
+                ("regula_falsi", 200, False, False)])
+    small = [abs(float(f(float(make_method(("base", nm))(f, a, b, 1e-12, 200)[0])))) < 1e-62
+             for nm in ("dekker", "illinois")]
+    check("Dekker and Illinois stall where |f| < 1e-62", small, [True, True])
+    # point 7: Table 3's two added rows
+    full = {r["label"]: r for r in _load("sweep_full.json")}
+    for lb, want_ in (("pure.exp_abs.bracket.bracket", (1848, 45, 0)), ("pure.exp_abs.bracket.credit", (1952, 45, 0))):
+        c = full[lb]["CHA"]
+        check(f"Table 3 row {lb}", (c["total"], c["solved"], c["over"]), want_)
+'''
+src = open(PATH, encoding="utf8").read()
+call_old = "    verify_controls()\n\n    print()"
+marker = '\n\nif __name__ == "__main__":\n    main()\n'
+assert src.count(call_old) == 1 and src.count(marker) == 1
+src = src.replace(call_old, "    verify_controls()\n    verify_revision2()\n\n    print()").replace(marker, FUNC + marker)
+open(PATH, "w", encoding="utf8").write(src)
+print("added verify_revision2")